scholarly journals Pair approximation model for the vaccination game: predicting the dynamic process of epidemic spread and individual actions against contagion

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200769
Author(s):  
Kazuki Kuga ◽  
Masaki Tanaka ◽  
Jun Tanimoto
Keyword(s):  
Dynamic Process ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Pair Approximation ◽  
Order Effects ◽  
Epidemic Spread ◽  
Underlying Network ◽  
Individual Actions ◽  
Individual Decisions

We successfully establish a theoretical framework of pairwise approximation for the vaccination game in which both the dynamic process of epidemic spread and individual actions in helping prevent social behaviours are quantitatively evaluated. In contrast with mean-field approximation, our model captures higher-order effects from neighbours by using an underlying network that shows how the disease spreads and how individual decisions evolve over time. This model considers not only imperfect vaccination but also intermediate protective measures other than vaccines. Our analytical predictions are validated by multi-agent simulation results that estimate random regular graphs at varying degrees.

How the heterogeneous infection rate effect on the epidemic spreading in activity-driven network

2016 ◽  
Vol 27 (06) ◽  
pp. 1650057 ◽  
Author(s):  
Dun Han ◽  
Dandan Li ◽  
Chao Chen ◽  
Mei Sun
Keyword(s):  
Infection Rate ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Epidemic Spread ◽  
Epidemic Threshold ◽  
Individual Activity ◽  
Immunization Strategies ◽  
The Individual ◽  
The Impact

In this paper, we research the impact of the heterogeneous infection rate on the epidemic spread in the activity-driven networks. By using the mean field approximation, the epidemic threshold is theoretically obtained. Several immunization strategies that could curb the epidemic spread are presented. Based on the theoretical analysis and simulation results, we obtain that the epidemic would be prevented effectively if the infection rate strongly correlates with the individual activity. However, if infection rate has a little correlation with the individual activity, most of the individuals may be infected. In addition, the epidemic can be suppressed soon if the individuals with high activity are immunized preferentially.

Connectivity dependence of gelation and elasticity in AB-type polymerization: an experimental comparison of the dynamic process and stoichiometrically imbalanced mixing

Soft Matter ◽  
2019 ◽  
Vol 15 (25) ◽  
pp. 5017-5025 ◽  
Author(s):  
Yuki Yoshikawa ◽  
Naoyuki Sakumichi ◽  
Ung-il Chung ◽  
Takamasa Sakai
Keyword(s):  
Dynamic Process ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Experimental Comparison

Comparison of two methodologies tuning the connectivity of AB-type polymerization shows the applicability of mean-field approximation.

PHASE DIAGRAMS AND CORRELATION INEQUALITIES OF A THREE-STATE STOCHASTIC EPIDEMIC MODEL ON THE SQUARE LATTICE

2006 ◽  
Vol 16 (12) ◽  
pp. 3687-3693 ◽  
Author(s):  
KAZUMICHI OHTSUKA ◽  
NORIO KONNO ◽  
NAOKI MASUDA ◽  
KAZUYUKI AIHARA
Keyword(s):  
Particle System ◽  
Contact Process ◽  
Mean Field ◽  
Field Approximation ◽  
Correlation Inequalities ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Pair Approximation ◽  
Stochastic Particle System ◽  
Stochastic Epidemic

We study a three-state stochastic particle system on the square lattice, which extends the contact process. The phase diagram is analyzed by the mean-field approximation, the pair approximation, and numerics. The pair approximation turns out to be better than the meanfield ansatz. We also show that the Harris-FKG type correlation inequalities approximately hold in the present model.

The Determination of the Magnetoelectric Coupling Coefficient in Ferroelectric–Ferromagnetic Composite Based on PZT–Ferrite

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk
Keyword(s):  
Dielectric Permittivity ◽  
Coupling Coefficient ◽  
Mean Field ◽  
Field Approximation ◽  
Theoretical Description ◽  
Magnetoelectric Coupling ◽  
Mean Field Approximation ◽  
Dielectric Measurements ◽  
Temperature Dependences ◽  
Multiferroic Composite

Abstract In the present work, the magnetoelectric coupling coefficient, from the temperature dependences of the dielectric permittivity for the multiferroic composite was determined. The research material was ferroelectric-ferromagnetic composite on the based PZT and ferrite. We investigated the temperature dependences of the dielectric permittivity (") for the different frequency of measurement’s field. From the dielectric measurements we determined the temperature of phase transition from ferroelectric to paraelectric phase. For the theoretical description of the temperature dependence of the dielectric constant, the Hamiltonian of Alcantara, Gehring and Janssen was used. To investigate the dielectric properties of the multiferroic composite this Hamiltonian was expressed under the mean-field approximation. Based on dielectric measurements and theoretical considerations, the values of the magnetoelectric coupling coefficient were specified.

scholarly journals Hexagonal-Shaped Spin Crossover Nanoparticles Studied by Ising-Like Model Solved by Local Mean Field Approximation

2021 ◽  
Vol 7 (5) ◽  
pp. 69
Author(s):  
Catherine Cazelles ◽  
Jorge Linares ◽  
Mamadou Ndiaye ◽  
Pierre-Richard Dahoo ◽  
Kamel Boukheddaden
Keyword(s):  
Spin Crossover ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ligand Field ◽  
Order And Disorder ◽  
The Matrix ◽  
Local Mean ◽  
Parameter Values

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.

Geometrical and Transport Properties of Disordered Fibre Networks: Analytical Results

1997 ◽  
Vol 11 (20) ◽  
pp. 867-875 ◽  
Author(s):  
A. A. Rodríaguez ◽  
E. Medina
Keyword(s):  
Probability Distribution ◽  
Transport Properties ◽  
Geometrical Structure ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Fracture Networks ◽  
Simplified Models ◽  
Fibre Density ◽  
Line Network

We study novel geometrical and transport properties of a 2D model of disordered fibre networks. To assess the geometrical structure we determine, analytically, the probability distribution for the number of fibre intersections and resulting segment sizes in the network as a function of fibre density and length. We also determine, numerically, the probability distribution of pore perimeters and areas. We find a non-monotonous behavior of the perimeter distribution whose main features can be explained by solving for two simplified models of the line network. Finally we formulate a mean field approximation to conduction, above the percolation threshold, using the derived results. Relevance of the results to fracture networks will be discussed.

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